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Low-temperature quantum bounds in simple models

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In the past few years there has been considerable activity around a set of quantum bounds on transport coefficients (viscosity, conductivity) and on chaos (Lyapunov exponents), relevant at low temperatures. The interest comes from the fact that AdS/CFT Black-Hole models seem to saturate all of them. To fix ideas, a simple case is that of systems whose lowest energy is a degenerate manifold, rather than a point. Examples are quantum hard-sphere liquids and quantum spin liquids. In this context the bounds are approached and are consequences of the uncertainty principle, and one understands the mechanisms whereby quantum mechanics enforces them. For a system to saturate the bound, it appears as a necessary condition that at each temperature there are some degrees of freedom that are still classical, and some are on the verge of being affected by quantum effects.

This talk is part of the Theory of Condensed Matter series.

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